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We consider a statistical model for pairs of traded assets, based on aCointegrated Vector Auto Regression (CVAR) Model. We extend standard CVARmodels to incorporate estimation of model parameters in the presence of priceseries level shifts which are not accurately modeled in the standard Gaussianerror correction model (ECM) framework. This involves developing a novel matrixvariate Bayesian CVAR mixture model comprised of Gaussian errors intra-day andAlpha-stable errors inter-day in the ECM framework. To achieve this we derive anovel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR)representation of Alpha-stable inter-day innovations. These results aregeneralized to asymmetric models for the innovation noise at inter-dayboundaries allowing for skewed Alpha-stable models.  Our proposed model and sampling methodology is general, incorporating thecurrent literature on Gaussian models as a special subclass and also allowingfor price series level shifts either at random estimated time points or known apriori time points. We focus analysis on regularly observed non-Gaussian levelshifts that can have significant effect on estimation performance instatistical models failing to account for such level shifts, such as at theclose and open of markets. We compare the estimation accuracy of our model andestimation approach to standard frequentist and Bayesian procedures for CVARmodels when non-Gaussian price series level shifts are present in theindividual series, such as inter-day boundaries. We fit a bi-variateAlpha-stable model to the inter-day jumps and model the effect of such jumps onestimation of matrix-variate CVAR model parameters using the likelihood basedJohansen procedure and a Bayesian estimation. We illustrate our model and thecorresponding estimation procedures we develop on both synthetic and actualdata.

Bayesian Cointegrated Vector Autoregression models incorporating  Alpha-stable noise for inter-day price movements via Approximate Bayesian  Computation